Described with admirable economy on Radio 1 the other day as 'all-round arty lady and Lou Reed's other half' (an item for years, the couple snuck off and married last month), Laurie Anderson has come a long, gadget-strewn way since her 1972 outdoor concert for 30 car horns, not forgetting 'Duet for door jamb and violin' (1976). Fifty film projectors a night at the height of the Reagan era bombarded opera-house audiences with thousands of images on enormous banks of screens that dwarfed their spiky-haired instigator – she with a microphone inside her mouth, say, trying to make her head sound like a cave; or speaking through a vocoder, or wearing goggles like headlamps, unable to see even as she lit her own precarious way along a narrow diving board suspended above the orchestra pit.

There are no state-of-the-art visuals in Homeland, Anderson's latest show; no funny goggles either (the vocoder, however, makes a welcome return). After 40 years in the multimedia avant garde, the hoi polloi have finally caught up; now everyone has a video backdrop, and Anderson – this may simply be coincidence – has decided they are a distraction. The only visuals tonight are a sea of flickering candles and ye olde dry ice, which swirls through a long, vertical spotlight that finds her still looking like the Little Prince: not much bigger than the mysterious console of keyboards and knobs she stands behind all evening, at the helm, a little out of reach, gently bending her knees in time with the music, twisting knobs then picking up her bow and leaning into a modified violin which makes sounds so big the Barbican seats vibrate. To her left, Eyvind Kang on viola; on her right, Icelandic bassist Skúli Sverrisson and Peter Scherer (keyboards); all three inscrutable, in black, adding depth and jazz to the mix.

Twiddling and fiddling, however, are only the half of it. What people really love about Laurie Anderson are the stories she tells, and the way she tells them: her singular lullaby voice a perennial balm (the singing is less easy to love); her humane, watchful wonder at the world – America in particular – and the mess it's in, conveyed through everyday tales that buttonhole the listener: 'You know, it takes a long time for a small bird to realise he's in a trap, but once he does he never stops [pause] shaking.'

And she is, while exuding buddhistic calm, angry. Her post-9/11 show was called Happiness. Homeland is named for the Bush administration's so-called security measures. Written on the road, it is both disjointed and grounded in familiar Anderson territory: language, technology, art, environment, freedom, fear. She kicks off with Aristophanes, picturing, over a delicate electronic gauze, a time before the earth existed ('no place to land because there is no land'), warm viola opening up the space, a pulsing, rubbery beat kicking in. 'I'm gonna break both your legs so you can't walk,' she promises, on 'Bad Guy' (one song merges into the next, pressing on, almost uninterrupted, for 90 minutes), 'I'm gonna put a bag over your head so you can't talk.' You realise there is no need for digital backdrops as all-too-familiar images from Iraq and Guantánamo flash up on cue inside your head. 'You thought there were things that had disappeared – beheadings and hangings,' says her old-man alter ego (her voice perfectly altered – a little bit Jimmy Stewart – shifting your perception of the words entirely), 'and suddenly they were everywhere.'

Targets are hit in quick succession, most notably in a litany of modern-day madness (war, the environment, Oprah) set to a cheeky disco beat. Kierkegaard, hotel rooms and overweight children go by; underwear models come down off billboards, airport security is regretted ('taking off your clothes in public could have been such fun...').

Over the years, Anderson has used plenty of personal stuff: the humiliating dreams, the scrapes with death (a fall down an open manhole, a childhood backflip on to concrete, a plane crash). There are touching glimpses of family in this show – her father 'with his diamond eyes, his voice life-size'; her grandmother 'in the pancake make-up she never wore in her life' – and moments of sparse beauty, too, as the violin magically spins its own web of accompanying lines. Anderson asks questions but doesn't claim to have the answers – except for religion, which, if it was down to her, would be all about snow.